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ABOUT FR-IRK SOFTWARE Improved Runge-Kutta (IRK) which is named FR-IRK software is a mathematical software for solving numerical solution of first order ordinary differential equations (ODEs) which arise in many fields of science such as physics, mechanics and etc. FR-IRK is programmed using the Maple. ADVANTAGES •FR-IRK software has less computational cost with higher error accuracy compared with existing classical code such as Runge-Kutta (RK) code which is one of the most popular numerical code for solving first order ODEs problems by scientists and in particular engineers. •FR-IRK program is designed with different orders from order 2 up to order 5, base on how much accuracy is required from clientele by considering the computational cost for solving the given IVPs.
COMMERCIAL POTENTIAL • FR-IRK software by using a new technique has less
computational cost and high error accuracy could be one of useful software for scientists for solving first order ODEs.
• FR-IRK software would be used by millions of academic institution for further development of their learning and research. Therefore, the academicians would constitute the largest clientele.
• FR-IRK software could form as a part of mathematical library routines as in Maple, Matlab , Mathematica and other mathematical software.
FR-IRK SOFTWARE MANUAL
Improved Runge-Kutta Method for Solving ODEs Software
Project Leader : Faranak Rabiei Co-Researchers : Fudziah Ismail, Mohamed Suleiman, Saeid Emadi Faculty : Institute for Mathematical Research, UPM Email : [email protected] Tel : 012-974 1134 Expertise: Numerical Analysis
IRK/RK(order of method) IRK2 RK2 IRK3 RK3 IRK4 IRK4-4 RK4 IRK5 RK6
Number of required stages 1 2 2 3 3 4 4 5 6
1. Go to the windows start menu and open the Maple-like software.
2. Close the Start-up and Quick Help windows.
7. See the results for the values of x, y. 6. In the opened common window chose “Function definition” and click on “Ok”.
3. Open the file from toolbar menu.
5. Run the programme. 4.5 Enter the appropriate step size length into h (For best accuracy normally h is 0
